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Left-orderable Fundamental Group and Dehn Surgery on the Knot $5_2$

  Published:2013-08-09
 Printed: Jun 2014
  • Ryoto Hakamata,
    Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
  • Masakazu Teragaito,
    Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
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Abstract

We show that the resulting manifold by $r$-surgery on the knot $5_2$, which is the two-bridge knot corresponding to the rational number $3/7$, has left-orderable fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords: left-ordering, Dehn surgery left-ordering, Dehn surgery
MSC Classifications: 57M25, 06F15 show english descriptions Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Ordered groups [See also 20F60]
57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45}
06F15 - Ordered groups [See also 20F60]
 

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